Reconsider Prob. 16.2-1.

C

(a) Use the routine Chapman-Kolmogorov Equations in your OR Courseware to find the n-step transition matrix P(n) for n 2, 5, 10, 20.

(b) The probability that it will rain today is 0.5. Use the results from part

(a) to determine the probability that it will rain n days from now, for n 2, 5, 10, 20.

C

(c) Use the routine Steady-State Probabilities in your OR Courseware to determine the steady-state probabilities of the state of the weather. Describe how the probabilities in the n-step transition matrices obtained in part

(a) compare to these steady-state probabilities as n grows large.